Automorphism groups of polycyclic-by-finite groups and arithmetic groups

We show that the outer automorphism group of a polycyclic-by-finite group is an arithmetic group. This result follows from a detailed structural analysis of the automorphism groups of such groups. We use an extended version of the theory of the algebraic hull functor initiated by Mostow. We thus make applicable refined methods from the theory of algebraic and arithmetic groups. We also construct examples of polycyclic-by-finite groups which have an automorphism group which does not contain an arithmetic group of finite index. Finally we discuss applications of our results to the groups of homotopy self-equivalences of K(\Gamma, 1)-spaces and obtain an extension of arithmeticity results of Sullivan in rational homotopy theory

AdS Strings with Torsion: Non-complex Heterotic Compactifications

Combining the effects of fluxes and gaugino condensation in heterotic supergravity, we use a ten-dimensional approach to find a new class of four-dimensional supersymmetric AdS compactifications on almost-Hermitian manifolds of SU(3) structure. Computation of the torsion allows a classification of the internal geometry, which for a particular combination of fluxes and condensate, is nearly Kahler. We argue that all moduli are fixed, and we show that the Kahler potential and superpotential proposed in the literature yield the correct AdS radius. In the nearly Kahler case, we are able to solve the H Bianchi using a nonstandard embedding. Finally, we point out subtleties in deriving the effective superpotential and understanding the heterotic supergravity in the presence of a gaugino condensate.Comment: 42 pages; v2. added refs, revised discussion of Bianchi for N

Numerical Study of Length Spectra and Low-lying Eigenvalue Spectra of Compact Hyperbolic 3-manifolds

In this paper, we numerically investigate the length spectra and the low-lying eigenvalue spectra of the Laplace-Beltrami operator for a large number of small compact(closed) hyperbolic (CH) 3-manifolds. The first non-zero eigenvalues have been successfully computed using the periodic orbit sum method, which are compared with various geometric quantities such as volume, diameter and length of the shortest periodic geodesic of the manifolds. The deviation of low-lying eigenvalue spectra of manifolds converging to a cusped hyperbolic manifold from the asymptotic distribution has been measured by $\zeta-$ function and spectral distance.Comment: 19 pages, 18 EPS figures and 2 GIF figures (fig.10) Description of cusped manifolds in section 2 is correcte

Two-dimensional model of dynamical fermion mass generation in strongly coupled gauge theories

We generalize the $N_F=2$ Schwinger model on the lattice by adding a charged scalar field. In this so-called $\chi U\phi_2$ model the scalar field shields the fermion charge, and a neutral fermion, acquiring mass dynamically, is present in the spectrum. We study numerically the mass of this fermion at various large fixed values of the gauge coupling by varying the effective four-fermion coupling, and find an indication that its scaling behavior is the same as that of the fermion mass in the chiral Gross-Neveu model. This suggests that the $\chi U\phi_2$ model is in the same universality class as the Gross-Neveu model, and thus renormalizable and asymptotic free at arbitrary strong gauge coupling.Comment: 18 pages, LaTeX2e, requires packages rotating.sty and curves.sty from CTA

Vibrational properties of phonons in random binary alloys: An augmented space recursive technique in the k-representation

We present here an augmented space recursive technique in the k-representation which include diagonal, off-diagonal and the environmental disorder explicitly : an analytic, translationally invariant, multiple scattering theory for phonons in random binary alloys.We propose the augmented space recursion (ASR) as a computationally fast and accurate technique which will incorporate configuration fluctuations over a large local environment. We apply the formalism to $Ni_{55}Pd_{45}$, Ni_{88}Cr_12} and $Ni_{50}Pt_{50}$ alloys which is not a random choice. Numerical results on spectral functions, coherent structure factors, dispersion curves and disordered induced FWHM's are presented. Finally the results are compared with the recent itinerant coherent potential approximation (ICPA) and also with experiments.Comment: 20 pages, LaTeX, 23 figure

Different HLA-DRB1 allele distributions in distinct clinical subgroups of sarcoidosis patients

<p>Abstract</p> <p>Background</p> <p>A strong genetic influence by the MHC class II region has been reported in sarcoidosis, however in many studies with different results. This may possibly be caused by actual differences between distinct ethnic groups, too small sample sizes, or because of lack of accurate clinical subgrouping.</p> <p>Subjects and methods</p> <p>In this study we HLA typed a large patient population (n = 754) recruited from one single centre. Patients were sub-grouped into those with Löfgren's syndrome (LS) (n = 302) and those without (non-Löfgren's) (n = 452), and the majority of them were clinically classified into those with recovery within two years (resolving) and those with signs of disease for more than two years (non-resolving). PCR was used for determination of HLA-DRB1 alleles. Swedish healthy blood donors (n = 1366) served as controls.</p> <p>Results</p> <p>There was a dramatic difference in the distribution of HLA alleles in LS compared to non-LS patients (p = 4 × 10^-36). Most notably, DRB1*01, DRB1*03 and DRB1*14, clearly differed in LS and non-LS patients. In relation to disease course, DRB1*07, DRB1*14 and DRB1*15 generally associated with, while DRB1*01 and DRB1*03 protected against, a non-resolving disease. Interestingly, the clinical influence of DRB1*03 (good prognosis) dominated over that of DRB1*15 (bad prognosis).</p> <p>Conclusions</p> <p>We found several significant differences between LS and non-LS patients and we therefore suggest that genetic association studies in sarcoidosis should include a careful clinical characterisation and sub-grouping of patients, in order to reveal true genetic associations. This may be particularly accurate to do in the heterogeneous non-LS group of patients.</p

Expansion in perfect groups

Let Ga be a subgroup of GL_d(Q) generated by a finite symmetric set S. For an integer q, denote by Ga_q the subgroup of Ga consisting of the elements that project to the unit element mod q. We prove that the Cayley graphs of Ga/Ga_q with respect to the generating set S form a family of expanders when q ranges over square-free integers with large prime divisors if and only if the connected component of the Zariski-closure of Ga is perfect.Comment: 62 pages, no figures, revision based on referee's comments: new ideas are explained in more details in the introduction, typos corrected, results and proofs unchange

Direct replacement of oral sodium benzoate with glycerol phenylbutyrate in children with urea cycle disorders

Long-term management of urea cycle disorders (UCDs) often involves unlicensed oral sodium benzoate (NaBz) which has a high volume and unpleasant taste. A more palatable treatment is licenced and available (glycerol phenylbutyrate [GPB], Ravicti) but guidance on how to transition patients from NaBz is lacking. A retrospective analysis of clinical and biochemical data was performed for eight children who transitioned from treatment with a single ammonia scavenger, NaBz, to GPB at a single metabolic centre; UCDs included arginosuccinic aciduria (ASA) (n = 5), citrullinaemia type 1 (n = 2) and carbamoyl phosphate synthetase I deficiency (CPS1) (n = 1). Patients transitioned either by gradual transition over 1–2 weeks (n = 3) or direct replacement of NaBz with GPB (n = 5). Median initial dose of GPB was 8.5 mL/m2/day based on published product information; doses were revisited subsequently in clinic and titrated individually (range 4.5–11 mL/m2/day). Pre-transition and post-transition mean ammonia levels were 37 μmol/L (SD 28 μmol/L) and 29 μmol/L (SD 22 μmol/L), respectively (p = 0.09), and mean glutamine levels were 664 μmol/L (SD 225 μmol/L) and 598 μmol/L (SD 185 μmol/L), respectively (p = 0.24). There were no reductions in levels of branched chain amino acids. No related adverse drug reactions were reported. Patients preferred GPB because of its lower volume and greater palatability. Direct replacement of NaBz with GPB maintained metabolic control and was simple for the health service and patients to manage. A more cautious approach with additional monitoring would be warranted in brittle patients and patients whose ammonia levels are difficult to control